Droves of U.S. voters are headed to polls across the country Tuesday to elect a new president, the culmination of a long, contentious campaign between Democrat Hillary Clinton and Republican Donald Trump.

Clinton, a former secretary of state looking to become the first female U.S. president, cast a ballot for herself at a polling place near her suburban New York home.

Trump, the blunt-spoken real estate tycoon making his first run for elected office, voted later near his skyscraper home a short distance away in the city, telling poll workers, "Everything's going great."

WATCH: Trump tells reporters he's "very excited" before voting

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Clinton said it was "the most humbling feeling" to vote. "I know how much responsibility goes with this and so many people are counting on the outcome of this election, what it means for our country, and I will do the best I can if I am fortunate enough to win today.”

WATCH: Clinton greets supporters, reporters after voting

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Her husband, former President Bill Clinton, accompanied her to the polling place to cast his vote as well, as did Trump's wife Melania at his polling station.

'Amazing process'

Trump, in a phone interview with Fox News, described the presidential campaign as an "amazing process," where he encountered the unfulfilled aspirations of many Americans. Trump said he had seen "so many hopes and dreams that didn't happen, that could have been helped with proper leadership."

At one of his debates with Clinton, Trump said would "keep you in suspense" about whether he would accept the result of the election unless he wins. Asked after voting what he would do if television networks call the election for Clinton, Trump said, "We'll see what happens."

The winner will become the country's 45th president, replacing President Barack Obama, a staunch Clinton supporter, when he leaves office January 20, limited by the U.S. Constitution to two terms in office.

The two candidates present voters with a vastly different choice. Clinton is the ultimate Washington insider, a fixture in the national capital for the last quarter century, as first lady, a U.S. senator and then the country's top diplomat for four years. Trump has built skyscrapers and casinos and wooed voters with an outsider's message, to upend the business-as-usual life in Washington.

Pre-election polls show Clinton with strong support from women, Hispanics and blacks and those with college degrees. Trump's following, the surveys show, to a large extent is coming from white working class men, those without college degrees and rural voters

Clinton headed to Election Day with a small, but steady advantage in national pre-election surveys, about a three-percentage edge, and small leads in several polls in key election states that will determine the outcome of the race.

U.S. presidential elections are not determined by the national popular vote, but rather by the results in each of the country's 50 states and the national capital, Washington. The most populous states have the biggest influence in the Electoral College, where the winning candidate must amass at least a majority 270 of the 538 electors.

WATCH: Electoral College is key

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More than 46 million ballots have already been cast in the many states that opened polling places for early voting in the last few weeks, with 80 million to 100 million more votes expected Tuesday. By early Tuesday evening the first vote counts will be disclosed from eastern states in the U.S., even as voting continues in the western part of the country.

Trump has alleged, without providing any evidence, that the election is "rigged" against him. His campaign late Monday filed suit in one western state, Nevada, claiming that election officials allowed early voting in the state to extend past closing time. However a judge ruled against the campaign on Tuesday.

In the first hours of Election Day, there were long lines of voters at polling stations throughout the country waiting to cast ballots, but otherwise only sporadic problems with malfunctioning voting machines in one state and technical issues with voter check-in in another.

Some female voters wore pantsuits to cast their votes for Clinton, a sartorial nod to her favorite outfits. Many of them were inspired by a Facebook group called Pantsuit Nation that supported the 69-year-old candidate who was the country's top diplomat from 2009 to 2013, during Obama's first term in the White House.

Clinton and the 70-year-old Trump, two of the three oldest candidates for the U.S. presidency, both finished their campaigns in the wee hours of Tuesday.

Clinton called the election "the test of our time," while Trump declared that "today is our Independence Day."

The events -- Clinton's in North Carolina and Trump's in Michigan -- were still going on when results came in from the first in-person voting on Election Day. Clinton got the most votes in the tiny New Hampshire town of Dixville Notch, just south of the Canadian border, beating Trump, 4 to 2.

Results

Results from the 50 U.S. states and the city of Washington will not be announced until after polls close in each one. By 8 p.m. Washington time (0100 GMT) polls will be closed in much of the eastern and central parts of the country, a group of states that accounts for more than half of the 538 electoral votes at stake.

Clinton struck a tone of unity in her final address in North Carolina, telling supporters she wants to be president for both those who vote for her and those who do not.

"Years from today, when your kids and grandkids ask what you did in 2016, when everything was on the line, you'll be able to say you voted for a stronger, fairer, better America," she said. "An America where we build bridges not walls, and where we prove conclusively that, yes love trumps hate."

Trump told his Michigan crowd that his win would bring "real change" to the country and allow working class people to "strike back" at what he said were corrupt politicians and special interests that have ruled the country.

"So the first thing we should do, let's get rid of Hillary, okay? That would be a very good first step," he said.

WATCH: Early a.m. drone video of polling station in Damascus, Maryland

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